Let's remember that while Kirk mucked about in the 20th century, he never created the sort of "uncontrolled" effects that would have significantly altered the future. He never prevented himself from being born, say, even though this would certainly be the consequence of removing a big war from the timeline. We're supposed to think that time in some mysterious way is self-healing, then, so that even the most blatant changes fail to create "ripple effects" of smaller changes.

Let me preface this by saying I'm a financial planner, not a physicist and most of my physics knowledge comes from a combination of Art Bell and the science channel. But I believe strongly in the butterfly effect. Look at Gillian Taylor. Yes, she may be a minor player in time. But suppose six months after she left she was meant to cause a car accident killing the man responsible (or even his mother before he was born). Or even something as small as Kirk delaying the double dumbass a few seconds.

On the other hand, McCoy did erase the entire UFP from existence by wandering around stoned in the 1930s. He apparently achieved that mainly through interacting with a "kingpin" figure, though; those might be rare and difficult to find, and simply killing a random bunch of, say, five thousand in any given era would not necessarily result in any sort of a noticeable change in history.

Again, I believe the smallest change can ripple through time like a snowball. One does not have to kill Hitler to prevent World War II nor does killing Rick Berman in 1990 prevent Voyager from being made.

But that would get them back to a timeline where there were no whales on Earth because nobody had traveled to the past to get any...

If OTOH Spock could guide them to a timeline where they had gone to the past, why didn't he do that right away so that they could have skipped the actual, troublesome going-to-past bit?

Consider string theory. The crew's involvement changed the vibration of that universe, creating an all new incredibly slightly different universe. When they returned, Spock (whose understanding of physics dwarfs Kaku and Hawking combined) would've realized this and made the proper adjustments. Imagine every universe as a highway. If one takes Highway A to Point B, which is now Highway B, does he not follow Highway A to get home?

I think you misunderestimate the effects of their incursion. "A Russian agent of an unknown organization somehow gets onto a US Navy nuclear destroyer totally undetected. Then, he somehow drains the reactor and has these odd gadgets our scientists can't figure out. Then he makes a run for it, escapes a fall that should've killed him and then is stolen from the hospital by a man with a lasor gun and a woman who matches the description of a missing whale biologist." You don't think that would cause some major concern from Washington, especially under Reagan?